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Atomic force microscopy (AFM) can be applied both in situ and ex situ to study the growth of crystals from solution. The method is particularly useful for investigating the crystallization of proteins, nucleic acids and viruses because it can be carried out in the mother liquor and in a non-perturbing fashion. Interactions and transformations between various growth mechanisms can be directly visualized as a function of supersaturation, as can the incorporation of diverse impurities and the formation and propagation of defects. Because the crystals can be observed over long periods, it is also possible to obtain precise quantitative measures of the kinetic parameters for nucleation and growth. Finally, AFM has allowed us to identify a number of previously unsuspected phenomena that influence nucleation, rate of growth and the ultimate perfection of macromolecular crystals. These are all features which are important in determining the ultimate resolution and quality of a crystal's diffraction pattern.

Satellite tobacco mosaic virus (STMV) can undergo at least two physical transitions that significantly alter its mechanical and structural characteristics. At high pH the 17-nm STMV particles expand radially by about 5 A to yield particles having diameters of about 18 nm. This pH-induced transition is further promoted by aging of the virions and degradation of the RNA, so that swollen particles ultimately appear even at neutral pH. While the native 17-nm particles crystallize as orthorhombic or monoclinic crystals which diffract to high resolution (1.8 A), the enlarged 18-nm particles crystallize in a cubic form which diffracts to no better than 5 A. In the transition, not only do the capsid protein subunits move radially outward, but the helical RNA segments with which they interact do as well. This is noteworthy because it demonstrates that the RNA and the protein shell are capable of coordinated movement, and that neither structure is rigidly defined or independent of the other. Using atomic force microscopy, it can be shown that STMV particles, upon drying, lose their mechanical rigidity and undergo deformation. Virions initially 17 nm in diameter shrink to more uniform final sizes than do 18 nm, initially swollen particles. This transition appears to be irreversible, as the particles do not reassume their former size nor structural rigidity upon rehydration. Evidence is also presented that preparations of native virus and their crystals are naturally somewhat heterogeneous and contain a variety of particles of anomalous size., (Copyright 2001 Academic Press.)

The structure of canavalin, the vicilin-class storage protein from jack bean, was refined to 1.7 A resolution in a highly twinned rhombohedral crystal of space group R3 and unit-cell parameters a = b = c = 83.0 A, alpha = beta = gamma = 111.1 degrees. The resulting R and R(free) were 0.176 and 0.245, respectively. The orthorhombic crystal structure (space group C222(1), unit-cell parameters a = 136.5, b = 150.3, c = 133.4 A) was also refined with threefold non-crystallographic symmetry restraints. R and R(free) were 0.181 and 0.226, respectively, for 2.6 A resolution data. No significant difference in the protein structure was seen between these two crystal forms, nor between these two and the hexagonal and cubic crystal forms reported elsewhere [Ko et al. (1993), Acta Cryst. D49, 478-489; Ko et al. (1993), Plant Physiol. 101, 729-744]. A phosphate ion was identified in the lumen of the C-terminal beta-barrel. Lattice interactions showed that the trimeric molecule could be well accommodated in both 'top-up' and 'bottom-up' orientations in a rhombohedral unit cell of the R3 crystal and explained the presence of a high twin fraction. The large inter-trimer stacking interface of the C222(1) crystal may account for its relative stability. Atomic force microscopy (AFM) investigations of the growth of three crystal forms of canavalin indicate the rhombohedral form to be unique. Unlike the other two crystal forms, it contains at least an order of magnitude more screw dislocations and stacking faults than any other macromolecular crystal yet studied, and it alone grows principally by generation of steps from the screw dislocations. The unusually high occurrence of the screw dislocations and stacking faults is attributed to mechanical stress produced by the alternate molecular orientations in the rhombohedral crystals and their organization into discrete domains or blocks. At boundaries of alternate domains, lattice strain is relieved by the formation of the screw dislocations.

Satellite tobacco mosaic virus (STMV) was probed using a variety of proteases. Consequences of the degradation were analyzed using gel electrophoresis, quasi-elastic light scattering (QELS), and atomic force microscopy (AFM). Proteolysis rates of 30 minutes for complete degradation of the protein capsid, up to many hours, were investigated. With each protease, degradation of virions 17 nm in diameter was shown by QELS to result in particles of 10 nm diameter, which is that of the RNA core observed in the virion by x-ray diffraction analysis. This was verified by direct visualization with atomic force microscopy. Using QELS, it was further shown that freshly prepared RNA cores remain as individual, stable, 10-nm condensed particles for 12 to 24 h. Clusters of particles then formed, followed by very large aggregates of 500 to 1000 nm diameter. AFM showed that the aggregates were composed of groups of the condensed RNA cores and were not due to unfolding of the nucleic acid. No unfolding of the core particles into extended conformation was seen by AFM until the samples were heated well beyond 90 degrees C. Mass spectrometry of RNA core particles revealed the presence of a major polypeptide whose amino acid sequence corresponded to residues 2 through 25 of the coat protein. Amino acids 13 through 25 were previously observed to be in direct contact with the RNA and are presumably protected from protease digestion. Low resolution difference Fourier analyses indicated the courses of the remainders of the amino terminal strands (amino acids 2-12) in intact virions. Any individual strand appears to have several choices of path, which accounts for the observed disorder at high resolution. These positively charged strands, serving as virtual polyamines, engage the helical segments of RNA. The intimate association of amino acid residues 2 through 25 with RNA likely contributes to the stability of the condensed conformation of the nucleic acid cores.

A chimeric human-simian IgG, antigen specific for CD4, when exposed to 0.5 M SO(=)(4) containing 0.4% polyethylene glycol or Jeffamine, self-assembles into discreet, roughly spherical particles 23 nm in diameter. Increasing SO(=)(4) to 1.55 M induces the IgG particles to crystallize in either a hexagonal or a monoclinic form. From X-ray diffraction, the former crystal is of space group P622, with one IgG particle in the unit cell; thus the particle itself must have 622 point group symmetry. Both crystal forms have been imaged using atomic force microscopy. Detailed features of the duodecamer were evident, including the symmetry and a large solvent channel along the sixfold axis. The particles in some ways resemble the hexameric IgG aggregates believed to activate compliment upon antigen binding and, therefore, may have physiological relevance. Investigation of seven other IgGs of diverse origins and subclasses indicates that many, if not most, IgGs form similar particles. To our knowledge, this is the first observation of the assembly of IgG into high symmetry aggregates in the absence of antigen or their crystallization., (Copyright 2000 Academic Press.)

In situ atomic force microscopy (AFM) was used to investigate surface evolution during the growth of single crystals of turnip yellow mosaic virus (TYMV). Growth of the (101) face of TYMV crystals proceeded by two-dimensional nucleation. The molecular structure of the step edges and adsorption of individual virus particles and their aggregates on the crystalline surface were recorded. The surfaces of individual virions within crystals were visualized and seen to be quite distinctive with the hexameric and pentameric capsomers of the T = 3 capsids being clearly resolved. This, so far as we are aware, is the first direct visualization of the capsomere structure of a virus by AFM. In the course of recording the in situ development of the crystals, a profound restructuring of the surface arrangement was observed. This transformation was highly cooperative in nature, but the transitions were unambiguous and readily explicable in terms of an organized loss of classes of virus particles from specific lattice positions. In some cases areas of a single crystal surface were recorded in which were captured successive phases of the transition. We believe this provides the first visual record of a cooperative restructuring of the surface of a supramolecular crystal.

Atomic force microscopy, in contact mode, has been used to image living mammalian cells in culture at both low and high resolutions. The method is shown practical for revealing cytoskeletal features beneath the cell membrane and their restructuring during a variety of cellular activities. Among the processes that we have visualized are locomotion, tissue formation, cell division, transformation by viruses, and cell death. We show that some processes that occur well within cells can, nonetheless, be observed using the atomic force probe. At high resolution, features on the cell surface on the order of 0.5 micron and their changes with time, can be recorded., (Copyright 1997 Academic Press.)

The crystallization of transfer RNA (tRNA) was investigated using atomic force microscopy (AFM) over the temperature range from 4 to 16 degrees C, and this produced the first in situ AFM images of developing nucleic acid crystals. The growth of the (110) face of hexagonal yeast tRNAPhe crystals was observed to occur at steps on vicinal hillocks generated by multiple screw dislocation sources in the temperature range of 13.5-16 degrees C. Two-dimensional nucleation begins to dominate at 13.5 degrees C, with the appearance of three-dimensional nuclei at 12 degrees C. The changes in growth mechanisms are correlated with variations in supersaturation which is higher in the low temperature range. Growth of tRNA crystals was characterized by a strong anisotropy in the tangential step movement and transformation of growth modes on single crystals were directly observed by AFM over the narrow temperature range utilized. Finally, lattice resolution images of the molecular structure of surface layers were recorded. The implications of the strong temperature dependence of tRNAPhe crystal growth are discussed in view of improving and better controlling crystallization of nucleic acids.

In the course of time-lapse video and atomic force microscopy (AFM) investigations of macromolecular crystal growth, we frequently observed the sedimentation of microcrystals and three-dimensional nuclei onto the surfaces of much larger, growing protein or virus crystals. This was followed by the direct incorporation over time of the smaller crystals into the bulk of the larger crystals. In some cases, clear indications were present that upon absorption of the small crystal onto the surface of the larger, there was proper alignment of the respective lattices, and consolidation proceeded without observable defect formation, i.e., the two lattices knitted together without discontinuity. In the case of at least one virus crystal, cubic satellite tobacco mosaic virus (STMV), addition of three-dimensional nuclei and subsequent expansion provided the principal growth mechanism at high supersaturation. This process has not been reported for growth from solution of conventional crystals. In numerous other instances, the lattices of the small and larger crystals were obviously misaligned, and incorporation occurred with the formation of some defect. This phenomenon of small crystals physically embedded in larger crystals could only degrade the overall diffraction and materials properties of macromolecular crystals.

The bifurcations of the periodic solutions of SEIR and SIR epidemic models with sinusoidally varying contact rate are investigated. The analysis is carried out with respect to two parameters: the mean value and the degree of seasonality of the contact rate. The corresponding portraits in the two-parameter space are obtained by means of a numerical continuation method. Codimension two bifurcations (degenerate flips and cusps) are detected, and multiple stable modes of behavior are identified in various regions of the parameter space. Finally, it is shown how the parametric portrait of the SEIR model tends to that of the SIR model when the latent period tends to zero.